SOLUTION: Hello. Find all x that will make f(x)= 0 f(x)= x^2 + 2x - 4 thanks!

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Question 189935: Hello.
Find all x that will make f(x)= 0
f(x)= x^2 + 2x - 4
thanks!
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=x%5E2%2B2x-4 Start with the given equation.


0=x%5E2%2B2x-4 Plug in f%28x%29=0


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=2, and c=-4


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%282%29+%2B-+sqrt%28+%282%29%5E2-4%281%29%28-4%29+%29%29%2F%282%281%29%29 Plug in a=1, b=2, and c=-4


x+=+%28-2+%2B-+sqrt%28+4-4%281%29%28-4%29+%29%29%2F%282%281%29%29 Square 2 to get 4.


x+=+%28-2+%2B-+sqrt%28+4--16+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-4%29 to get -16


x+=+%28-2+%2B-+sqrt%28+4%2B16+%29%29%2F%282%281%29%29 Rewrite sqrt%284--16%29 as sqrt%284%2B16%29


x+=+%28-2+%2B-+sqrt%28+20+%29%29%2F%282%281%29%29 Add 4 to 16 to get 20


x+=+%28-2+%2B-+sqrt%28+20+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-2+%2B-+2%2Asqrt%285%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-2%29%2F%282%29+%2B-+%282%2Asqrt%285%29%29%2F%282%29 Break up the fraction.


x+=+-1+%2B-+sqrt%285%29 Reduce.


x+=+-1%2Bsqrt%285%29 or x+=+-1-sqrt%285%29 Break up the expression.


So the answers are x+=+-1%2Bsqrt%285%29 or x+=+-1-sqrt%285%29


which approximate to x=1.236 or x=-3.236

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Find all x that will make f(x)= 0
f(x)= x^2 + 2x - 4
------------------------
x^2+2x-4 = 0
Use the quadratic formula to get:
x = [-2 +- sqrt(2^2 - 4*1*-4)]/2
---
x = [-2 +- sqrt(20)]/2
x = [-2 +- 2sqrt(5)]/2
x = [-1 +- sqrt(5)]
============================
Cheers,
Stan H.